Situation #1: This first figure shows "Newton's Mountain," so high that its top is above the drag of the atmosphere. The cannonball is fired and hits the ground as shown.

Describe its path as the cannon is fired faster and faster, but still less than 8 km/s.

What is the shape of its trajectory when it is fired at exactly 8 km/s? Why?

What would be the shape of the orbital path if the cannonball were fired at a speed of about 9 km/s?

Refer to the following information for the next seven questions.

Situation #2: This second figure shows a satellite in circular orbit.

Mentally draw at each of the four positions a vector that represents the gravitational force, F, exerted on the satellite. Then mentally draw at each position a vector that represents the velocity, v, of the satellite.

Are all four force vectors the same length? Why or why not?

Are all four velocity vectors the same length? Why or why not?

What is the angle between each set of F and v vectors? Is there any component of F along v?

What does this tell you about the work the force of gravity does on the satellite?

Does the KE of the satellite remain constant, or does it vary?

Does the PE of the satellite remain constant, or does it vary?

Refer to the following information for the next nine questions.

Situation #3: This final figure shows a satellite in elliptical orbit.

Repeat the procedure you used for the circular orbit, mentally drawing vectors F and v for each position shown.

Are your vectors F all the same magnitude? Why or why not?

Are your vectors v all the same magnitude? Why or why not?

Is the angle between vectors F and v everywhere the same, or does it vary?

Are there places where there is a component of F along v?

Is work done on the satellite when there is a component of F along and in the same direction of v?

If so, what happens to the KE of the satellite?

When there is a component of F along and opposite to the direction of v, what happens to the KE of the satellite?